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Visualizing the impact of two-seat districts

In response to my post about the two-seat districts in Burkina Faso, David Altman (a leading scholar on Chilean and comparative politics) contacted me to say I was not quite right in my contention that the Chilean experience showed that two-seat districts systematically advantage the second party or bloc. Fair enough. I made my point utterly without nuance–as if the second list was always advantaged more than the first–and I elided the distinction between national and district-level effects.

David showed me a graph he had generated in which it is clear that, on average, there is little difference between the vote-seat gap for the main center-left alliance and that of the right-wing alliance; in fact, the gap tended to be slightly higher for the center-left. It is the right that has been consistently second in nationwide votes, so the data seemed to challenge my “systematic” claim.

In the Burkina Faso post, I went over a number of examples from the district level in that country where there was a large advantage in terms of the translation of votes into seats for the second party. I do not think David and I disagree about the district-level effects. But what about the national?

For reasons Taagepera and Laakso* first emphasized in 1980, the best way to visualize how electoral systems treat parties (or alliances) is not by using the difference between seat and vote shares for each party, but by the advantage ratio, A:

A=(percent seats)/(percent votes).

This is the approach I will use here. The first graph simply plots the distribution of A values in the Chilean elections from 1989 to 2013 (Chamber of Deputies only), using a kernel density plot. It also marks the arithmetic means with vertical dashed lines.

Of course, with only seven elections, we should be cautious in interpreting how “systematic” the effect is. Yet the trend is clear: the right-wing alliance (referred to in the graph as “Alianza” and shown in blue) has a notable tendency to have higher advantage ratios than has the center-left (“Concertación”).** Yet in every election the Alianza has been second in nationwide votes, albeit by widely varying margins.

The second graph shows the advantage ratio against the nationwide gap in votes between the two parties (Concertación vote share minus Alianza vote share), with each election labelled.

Note that as the gap grows, there is a tendency of the Alianza’s advantage ratio to increase. There is actually a small such tendency for the Concertación, too, although it is much closer to a flat line. More importantly, we would normally expect that as the top two parties/alliances grow farther apart in votes, the first one would gain more in seat share. Yet what the Chilean pattern shows us is that the second one gains more, relative to its vote share, as the gap grows. This is not something we would expect under any other district magnitude (except maybe M=4) under any proportional (or semi-proportional) allocation rule. It is this “relative to its vote share” point that I meant to convey. Two-seat districts are a good way to get the second force more over-representation than that of the first force.

If we turn to individual elections, we see that Alianza data point is higher than that for the Concertación in 1989, 1993, and 2005, all years in which the Alianza was more than ten percentage points behind the Concertación, plus in 2009 when the two alliances were almost even in votes. On the other hand, the large vote gap for the Concertación in two elections, 1997 and 2013, resulted in a higher advantage ratio for the Concertación. In 2013 I assume that has to do with the center-left having expanded its electoral reach by incorporating new parties and rebranding its list as Nueva Mayoría. I am not sure what the explanation is in 1997; the gap was large that year, but as the data plot shows, not unusually so.

I find it interesting that the worst year for the Concertación, by this standard, was 2005, which I had noted at the time as being unusual in having a bloc of parties compete against each other in the first round of the presidential elections while remaining united on legislative lists–the Alianza’s two main component parties had separate presidential candidates. The result in the legislative races was their best advantage ratio since the first democratic election of 1989.

It looks to me like two-seat districts in Chile have indeed generated a systematic greater advantage to the second alliance over the first, even if the effect is tempered by other features of specific elections.

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* Rein Taagepera and Markku Laakso, “Proportionality Profiles of West European Electoral Systems,” European Journal of Political Research 8 (1980):423-46; see also Rein Taagepera and Matthew S. Shugart, Seats and Votes: The Effects and Determinants of Electoral Systems (Yale University Press, 1989), in particular chapter 7.

** The right has run under different names in different elections. I am using “Alianza”; the center-left changed names from Concertación to Nueva Mayoría in 2013.

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3 thoughts on “Visualizing the impact of two-seat districts”

To start a little controversy, I will repeat an over-simplified conclusion I reached long ago: “Chile’s two-seaters tend to elect one left candidate and one right candidate, making a tie. But then a handful of wealthy constituencies, where the right has more than 66% of the votes, elect two right-wingers. A PR system only General Pinochet could love (he invented it).”

That’s basically correct, Wilf, as regards the initial objectives behind the system. In fact, I will relay an anecdote: I met an official of the US Federal Electoral Commission some time around 1988 who had served as an advisor to the Pinochet government as they were devising an electoral law. He said their request had been for a system that would (in the words of the person I met) “screw the left”.

Nonetheless, we should not lose sight of the fact that the center-left alliance has won a majority of Chamber seats (and, I think, of elected Senate seats) all but once. And I believe the Concertacion generally wins both seats in more districts than does the right, due to its dominance in urban areas. In 2005, for example (a year for which I have the data handy, and in which the right had a high advantage ratio, as shown above), there were six Chamber districts where the center-left won two seats and only one where the right did.

I might add that it is not necessary to have more than 66% of the votes to win both seats in a district (as I have often seen it stated). It is necessary to have double the votes of the second list. Given that there are usually several lists running, the effective requirement for two seats is somewhat lower than 66%. In the 2005 example, the lists that won two seats in a district averaged 63% and had as low as 58%.